In the operation of a tool of this type, the mandrel is connected to an expansion rod of the grinding machine. As the mandrel penetrates further into the sleeve, its sloping surfaces move the bars radially outward as the tool expands. When the tool comprises springs which tend to hold the bars against the sloping guide surfaces and which retract these bars inward when the mandrel is withdrawn, the radial position of the bars and consequently the working diameter of the tool are positively determined when the mandrel is thrust forward but not when it is withdrawn; this is due to the frictional resistance opposing the retraction of the bars.